Optimized Symmetric Bicompact Scheme of the Sixth Order of Approximation with Low Dispersion for Hyperbolic Equations

Abstract

A dispersion analysis of semidiscrete schemes from the one-parameter family of symmetric bicompact schemes of the sixth order of accuracy in space is performed. In this family, a scheme is found that has the smallest maximum phase error in the entire range of wavelengths resolvable on an integer-node grid. The maximum phase error of this optimized scheme does not exceed one-hundredth of percent. A numerical example is presented that demonstrates the ability of the bicompact scheme to adequately simulate short wave propagation on coarse grids at long times.